How do I get rid of unwanted corners inside a bent tube?
I think this is a great question, because it applies to real-life engineering too. Before getting rid of that troubled geometry it helps to understand why it happens in the first place.



Problem

The reason for the overlapping geometry is that the radius of those bends is smaller than the radius of the tube minus the thickness. 

Radius of tube exceeds bend radius:



Resolution

Either make the bends bigger or the radius of the tube smaller. If you want a tight corner tweak them so that the bend radius is about the same as the tube radius (plus or minus the tube thickness). Then use the solidify modifier in the offset direction which allows you to give it thickness (either offset towards the inside, or outside)

See: just about right



Whether you use bezier or spun geometry, is really down to personal taste. The bezier approach allows you to quickly edit your path, and while it will not give perfect arc bends mathematically, that might not matter for your purposes. If you are to simulate real tubing, that too is almost never perfect arc.

If you need to make a lot of tubing here's a blend that uses the sverchok  parametric addon, it lets you adjust the tube radius and bend radius on the fly till you get it right.